Column density distribution function in the Cygnus-X North cloud (left panel) and the Polaris Flare cloud (right panel). The full red lines in both panels show a fit by a lognormal function in the low column density regime (≲ 5 × 10²¹ cm⁻² in Cygnus-X North and ≲1 × 10²¹ cm² in Polaris). The dashed line is a fit to the power-law regime that is observed in both regions in the intermediate column density regime, while the triple-dot dashed red line in the case of the Cygnus-X North region is a fit to the shallower power law in the high column density regime.